6 ms·

As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics the

As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.

chneu 20d ago
Lowering the bar for the masses isn't always a good thing
- PeterWhittaker 20d ago
  Examples, preferably academic?
  - applfanboysbgon 20d ago
    Half of modern academia, for one. Universities have turned into degree mills with the expectation that >50% of the population requires a college degree, regardless of whether they actually have any interest or need for one beyond doing it because it's a prerequisite for a good career, independent of whether said career actually uses the knowledge in any way. Not that I actually agree that math was at the right level of gatekeeping. It definitely feels intentionally opaque beyond reason, and I think it's why LLMs are able to cut through the obfuscation and solve problems that maybe wouldn't actually have been considered quite so hard if mathematicians did a better job of making their work accessible.
    - JoeAltmaier 20d ago
      <pedant>28% of adult Americans</pedant>
      - applfanboysbgon 20d ago
        66% in Japan. Who said anything about America?
        JoeAltmaier 19d ago
        You know, where most of the universities are. And, who said anything about Japan? Confused.
  - bayindirh 20d ago
    We have seen the thing in programming. I'm not a gatekeeper, I love seeing more people to code. On the other hand, along the way, we lost the joy of the journey and only fixated at the destination. Result is more software at lower quality. The reason is statistics. When you increase the population, you increase the population of every kind of programmer, and people who want the result are favored in most competitive sectors because corporations want something somewhat working yesterday. ...and here we are. Now programmers talking about code quality is stoned en-masse. If it's somewhat working then it's good. Efficiency, resiliency, maintainability and sustainability is an afterthought. Some of my friends who loved debating programming language theory now don't even care about the code. They don't write it, just vibe, and they don't plan to come back to "older, caveman style of development". Some universities are also adding fuel to the fire: They "prepare students for the job", not teaching the science, but the parts that corporations need for the job only. Though, hardware was cheap and people were expensive, and now code is cheap and hardware is expensive now. We'll see.
    - mathisfun123 20d ago
      this comparison makes little sense. > we lost the joy of the journey and only fixated at the destination. that's because you can make money with code and so it went the same way as everything else that's capitalized/commodified. here a better comparison would be art which is generally still pursued on its own merits/pleasures.
      - bayindirh 20d ago
        The point I was trying to make was not "enjoying the process for the sake of it", but paying attention and spending effort on the journey created better software at the end. When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications. Now we slap what we found online together and calling it done. Everything is sparse, takes ages to load, centuries to submit and everything is so disconnected and async that some simple features are straight out impossible. This is what fixating on the destination brought us. I dare you to download something you purchased 3 months ago via a 4096 character S3 link they have sent you, and double dare you to ask customer support for a new link. I'll bet that with a 80% chance they have no way to verify your serial number, even.
- waynecochran 20d ago
  It is not lowering the bar to find better ways to demystify and explain things. In fact, I would say those who can explain it well understand it the best. Richard Feynman would be my best example.
  - tuckerman 20d ago
    Do you have any examples of places you felt like there was a lot of gatekeeping? Perhaps having studied mathematics I am a bit blind to the issue here and would like to learn more. I agree making simple things sound complicated to appear more impressive is bad but there are limits. Even with Feynman he could only go so far, e.g. his interview about why questions and magnetism.
    - waynecochran 20d ago
      I am not thinking of intentional gatekeeping, but more of the kind where mathematicians build themselves their own island of concepts and notation with no thought of building a passageway for others to engage and make use of the theory. I would find modern algebraic geometry highly useful as someone who works in computer graphics and computer vision, but much of the theory is akin to learning a new language and I don't get the sense that those who publish their work in this field care if I enter their world.
      - tuckerman 20d ago
        Ah that's fair. I do think in a lot of fields there is a lot of impact/influence to be had by people who are willing to do work to bridge different fields. I wonder to what degree this is because practitioners don't always see how their work could be used elsewhere.
  - ifethereal 20d ago
    I would say that it is lowering the bar to "find better ways to demystify and explain things." But there is no harm to this bar falling, because this is a bar for entry. There is a separate bar for making research discoveries (being credited for them, specifically), and that one should not be lowered, because it is a bar of standards.
- deleted 20d ago
  [deleted]
Jblx2 20d ago
Kind of makes me think of Arnold's, "On Teaching Mathematics": https://www.maths.tcd.ie/pub/Maths/Courseware/ProblemSolving/Arnold/TeachingMathematics.pdf https://www.maths.tcd.ie/pub/Maths/Courseware/ProblemSolving...
- godelski 20d ago
  > Mathematics is a part of physics This feels backwards. I frequently joke "physics is the subset of mathematics that reflects the observable world". Math can be as abstract as it wants, but physics has a constraint. It must model an observable world (related, this us part of why people say String Theory is math and not physics)
  - GregBuchholz 20d ago
    What about the next 3,900 words after the first sentence? (yes, it is that V.I. Arnold https://en.wikipedia.org/wiki/Vladimir_Arnold https://en.wikipedia.org/wiki/Vladimir_Arnold )
    - godelski 20d ago
      > What about the next 3,900 words after the first sentence? But had I read those I wouldn't have been able to feel smart with egg all over my face.
Tazerenix 20d ago
I think you're a little naive if you think this is because of gate-keeping by mathematicians rather than the essential complexity of mathematics. Mathematicians individually and as a group would love nothing more than a world which is capable of understanding their work more deeply. In the exact same way that LLMs allow anyone to vibe code an app but do not replace real understanding of system design due to its essential complexity, non-mathematicians will quickly learn that asking an LLM to pump out advanced mathematical statements to you, even if they are correct (and even if you could verify them) does not constitute understanding, and that the human brain is the bottleneck either way. It is only if the LLM is super-human at simplification and explaining that a difference will be noted. This would be excellent for mathematics but its not a foregone conclusion (and the argument of most mathematicians, such as Terence Tao, is that this distillation process is one of the key parts of doing mathematics, and that LLMs so far seem to be going in the opposite direction. I suspect its probably user error and leveraging the tools better will produce different outcomes, but mathematicians are only just starting the journey that software developers have been going through, so patience is needed).
- waynecochran 20d ago
  Folks keep using the word "gate keeping" -- I never used that term nor implied intentional gate keeping. It's simply not caring if those outside the club understand -- there is no one guarding the door its just folks don't care if anyone finds it.
  - bonoboTP 19d ago
    Gatekeeping is a human universal. Even those who preach maximum inclusion do exclude plenty, of course there is always explanation why that doesn't count. If you try to run any community you quickly learn the importance of gatekeeping. Eternal September etc. See any site or fandom that gets mainstream etc. I don't think anyone has any duty to actively pull in as many as possible new people. Zen masters used to chase away students or make them sit on their doorstep for days and send them away anyway. Now, the west is essentially Christian and so the missionary impulse is real, but it doesn't work without the other stuff in the package.
joe_the_user 20d ago
I too have a degree in math and it's easy to see some of what's happening as too much of an emphasis on intellectual chest thumping and to little emphasis on showing why understanding the concepts is useful for everyone. I will say the problem may well increased here by the American education system which denigrates such understanding and isn't influenced by mathematicians. But also, with things rapidly changing, perhaps in ten years chat programs will not only do superhuman but make their proofs marvelously accessible and provide incredible tutoring sufficient to bring any curious up to a super high level quickly. Then what can you say and what can you complain of. But I think "do everything machines" are necessarily inevitable but the situation does make it uncertain where the limits are.
lo_zamoyski 20d ago
I would say the research university is getting comeuppance. Pedagogy is the primary purpose of educational institutions. That includes universities. However, when research is placed first, you are often left with mediocre teachers, because "who cares?" They were hired to do research and lend the university that kind of prestige; teaching is an afterthought squeezed into the spaces that remain. And frankly, we haven't the faintest clue today what education is even for. That doesn't bode well. Add to this the other troubles facing the university, like declining attendance, skyrocketing costs, and AI cheating and we're in for a very interesting transition indeed.
godelski 20d ago
Not everyone needs to be a communicator. Why should we expect everyone to be both a great researcher and communicator? The obvious result is that it is as effective as engineering managers. Sure, there's some amazing ones, but most aren't. Though that also doesn't mean no expertise in the field (i.e. non-engineering manager) is any better. It is just that managing/communicating is a different and orthogonal skill. What needs to happen is we need to make it okay for people to specialize in more things. More nuance to this rather than trying to throw everyone into nice easy to manage buckets. Those buckets are just unrealistic abstractions filled with hope, denial, and laziness. Reality is surprisingly complex. Math can do a really good job helping you understand that, but it's a sufficient condition, not a necessary one
skew-aberration 20d ago
Never been my experience of maths, which is one of the most accessible disciplines to have ever existed. I also have a degree, but mostly taught myself the important undergrad-level concepts as a kid. I just went to the library and borrowed any of the hundreds of books written to clearly communicate maths to beginners or downloaded any of the free ebooks / lecture notes. Name a single field of endeavor that is more open in 2026. Software certainly isn't one of them - the best stuff has always been gatekept.

chneu 20d ago

Lowering the bar for the masses isn't always a good thing

PeterWhittaker 20d ago
Examples, preferably academic?
- applfanboysbgon 20d ago
  Half of modern academia, for one. Universities have turned into degree mills with the expectation that >50% of the population requires a college degree, regardless of whether they actually have any interest or need for one beyond doing it because it's a prerequisite for a good career, independent of whether said career actually uses the knowledge in any way. Not that I actually agree that math was at the right level of gatekeeping. It definitely feels intentionally opaque beyond reason, and I think it's why LLMs are able to cut through the obfuscation and solve problems that maybe wouldn't actually have been considered quite so hard if mathematicians did a better job of making their work accessible.
  - JoeAltmaier 20d ago
    <pedant>28% of adult Americans</pedant>
    - applfanboysbgon 20d ago
      66% in Japan. Who said anything about America?
      - JoeAltmaier 19d ago
        You know, where most of the universities are. And, who said anything about Japan? Confused.
- bayindirh 20d ago
  We have seen the thing in programming. I'm not a gatekeeper, I love seeing more people to code. On the other hand, along the way, we lost the joy of the journey and only fixated at the destination. Result is more software at lower quality. The reason is statistics. When you increase the population, you increase the population of every kind of programmer, and people who want the result are favored in most competitive sectors because corporations want something somewhat working yesterday. ...and here we are. Now programmers talking about code quality is stoned en-masse. If it's somewhat working then it's good. Efficiency, resiliency, maintainability and sustainability is an afterthought. Some of my friends who loved debating programming language theory now don't even care about the code. They don't write it, just vibe, and they don't plan to come back to "older, caveman style of development". Some universities are also adding fuel to the fire: They "prepare students for the job", not teaching the science, but the parts that corporations need for the job only. Though, hardware was cheap and people were expensive, and now code is cheap and hardware is expensive now. We'll see.
  - mathisfun123 20d ago
    this comparison makes little sense. > we lost the joy of the journey and only fixated at the destination. that's because you can make money with code and so it went the same way as everything else that's capitalized/commodified. here a better comparison would be art which is generally still pursued on its own merits/pleasures.
    - bayindirh 20d ago
      The point I was trying to make was not "enjoying the process for the sake of it", but paying attention and spending effort on the journey created better software at the end. When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications. Now we slap what we found online together and calling it done. Everything is sparse, takes ages to load, centuries to submit and everything is so disconnected and async that some simple features are straight out impossible. This is what fixating on the destination brought us. I dare you to download something you purchased 3 months ago via a 4096 character S3 link they have sent you, and double dare you to ask customer support for a new link. I'll bet that with a 80% chance they have no way to verify your serial number, even.
waynecochran 20d ago
It is not lowering the bar to find better ways to demystify and explain things. In fact, I would say those who can explain it well understand it the best. Richard Feynman would be my best example.
- tuckerman 20d ago
  Do you have any examples of places you felt like there was a lot of gatekeeping? Perhaps having studied mathematics I am a bit blind to the issue here and would like to learn more. I agree making simple things sound complicated to appear more impressive is bad but there are limits. Even with Feynman he could only go so far, e.g. his interview about why questions and magnetism.
  - waynecochran 20d ago
    I am not thinking of intentional gatekeeping, but more of the kind where mathematicians build themselves their own island of concepts and notation with no thought of building a passageway for others to engage and make use of the theory. I would find modern algebraic geometry highly useful as someone who works in computer graphics and computer vision, but much of the theory is akin to learning a new language and I don't get the sense that those who publish their work in this field care if I enter their world.
    - tuckerman 20d ago
      Ah that's fair. I do think in a lot of fields there is a lot of impact/influence to be had by people who are willing to do work to bridge different fields. I wonder to what degree this is because practitioners don't always see how their work could be used elsewhere.
- ifethereal 20d ago
  I would say that it is lowering the bar to "find better ways to demystify and explain things." But there is no harm to this bar falling, because this is a bar for entry. There is a separate bar for making research discoveries (being credited for them, specifically), and that one should not be lowered, because it is a bar of standards.
deleted 20d ago
[deleted]

Jblx2 20d ago

Kind of makes me think of Arnold's, "On Teaching Mathematics": https://www.maths.tcd.ie/pub/Maths/Courseware/ProblemSolving/Arnold/TeachingMathematics.pdf https://www.maths.tcd.ie/pub/Maths/Courseware/ProblemSolving...

godelski 20d ago
> Mathematics is a part of physics This feels backwards. I frequently joke "physics is the subset of mathematics that reflects the observable world". Math can be as abstract as it wants, but physics has a constraint. It must model an observable world (related, this us part of why people say String Theory is math and not physics)
- GregBuchholz 20d ago
  What about the next 3,900 words after the first sentence? (yes, it is that V.I. Arnold https://en.wikipedia.org/wiki/Vladimir_Arnold https://en.wikipedia.org/wiki/Vladimir_Arnold )
  - godelski 20d ago
    > What about the next 3,900 words after the first sentence? But had I read those I wouldn't have been able to feel smart with egg all over my face.

Tazerenix 20d ago

I think you're a little naive if you think this is because of gate-keeping by mathematicians rather than the essential complexity of mathematics. Mathematicians individually and as a group would love nothing more than a world which is capable of understanding their work more deeply. In the exact same way that LLMs allow anyone to vibe code an app but do not replace real understanding of system design due to its essential complexity, non-mathematicians will quickly learn that asking an LLM to pump out advanced mathematical statements to you, even if they are correct (and even if you could verify them) does not constitute understanding, and that the human brain is the bottleneck either way. It is only if the LLM is super-human at simplification and explaining that a difference will be noted. This would be excellent for mathematics but its not a foregone conclusion (and the argument of most mathematicians, such as Terence Tao, is that this distillation process is one of the key parts of doing mathematics, and that LLMs so far seem to be going in the opposite direction. I suspect its probably user error and leveraging the tools better will produce different outcomes, but mathematicians are only just starting the journey that software developers have been going through, so patience is needed).

waynecochran 20d ago
Folks keep using the word "gate keeping" -- I never used that term nor implied intentional gate keeping. It's simply not caring if those outside the club understand -- there is no one guarding the door its just folks don't care if anyone finds it.
- bonoboTP 19d ago
  Gatekeeping is a human universal. Even those who preach maximum inclusion do exclude plenty, of course there is always explanation why that doesn't count. If you try to run any community you quickly learn the importance of gatekeeping. Eternal September etc. See any site or fandom that gets mainstream etc. I don't think anyone has any duty to actively pull in as many as possible new people. Zen masters used to chase away students or make them sit on their doorstep for days and send them away anyway. Now, the west is essentially Christian and so the missionary impulse is real, but it doesn't work without the other stuff in the package.

joe_the_user 20d ago

I too have a degree in math and it's easy to see some of what's happening as too much of an emphasis on intellectual chest thumping and to little emphasis on showing why understanding the concepts is useful for everyone. I will say the problem may well increased here by the American education system which denigrates such understanding and isn't influenced by mathematicians. But also, with things rapidly changing, perhaps in ten years chat programs will not only do superhuman but make their proofs marvelously accessible and provide incredible tutoring sufficient to bring any curious up to a super high level quickly. Then what can you say and what can you complain of. But I think "do everything machines" are necessarily inevitable but the situation does make it uncertain where the limits are.

lo_zamoyski 20d ago

I would say the research university is getting comeuppance. Pedagogy is the primary purpose of educational institutions. That includes universities. However, when research is placed first, you are often left with mediocre teachers, because "who cares?" They were hired to do research and lend the university that kind of prestige; teaching is an afterthought squeezed into the spaces that remain. And frankly, we haven't the faintest clue today what education is even for. That doesn't bode well. Add to this the other troubles facing the university, like declining attendance, skyrocketing costs, and AI cheating and we're in for a very interesting transition indeed.

godelski 20d ago

Not everyone needs to be a communicator. Why should we expect everyone to be both a great researcher and communicator? The obvious result is that it is as effective as engineering managers. Sure, there's some amazing ones, but most aren't. Though that also doesn't mean no expertise in the field (i.e. non-engineering manager) is any better. It is just that managing/communicating is a different and orthogonal skill. What needs to happen is we need to make it okay for people to specialize in more things. More nuance to this rather than trying to throw everyone into nice easy to manage buckets. Those buckets are just unrealistic abstractions filled with hope, denial, and laziness. Reality is surprisingly complex. Math can do a really good job helping you understand that, but it's a sufficient condition, not a necessary one

skew-aberration 20d ago

Never been my experience of maths, which is one of the most accessible disciplines to have ever existed. I also have a degree, but mostly taught myself the important undergrad-level concepts as a kid. I just went to the library and borrowed any of the hundreds of books written to clearly communicate maths to beginners or downloaded any of the free ebooks / lecture notes. Name a single field of endeavor that is more open in 2026. Software certainly isn't one of them - the best stuff has always been gatekept.